Within the first 2 minutes of the film, the Archbishop brings "The Mikado" record into his den/office and puts it on. He puts the sleeve of the record inside the stereo on top of some other, stacked, records. The stereo has a cross on it. As he turns around, the sleeve is on his desk, not his stereo.
When Gloria and Detective Carlson are leaving to go to the theater, Carlson says that Gloria must come with because she is the only one who can identify Whitey Jackson (he says that she is the only one who has seen him) even though he had previously seen a photograph of Whitey Jackson.
In "The Mikado", Yum-Yum, Peep-Bo, and Pitti-Sing are shown performing "Three Little Maids from School". The film then cuts to Tony and Gloria racing to the opera house. During this time Tony has time to drive several blocks, crash the cowboy's truck, survey the scene and commandeer an airport limo. When the film cuts back to the Mikado performance, only a few seconds have elapsed in the song.
When Gloria escapes from being kidnapped, she's about to open the window when her right comb starts to fall out of her hair, unpinning the right side of her hairdo. In the next shot when she's opening the window, the comb and her hair are back in place.
When Gloria is escaping from the apartment where she's being held, she punches Turk in the right side of the face with the brass knuckles, but when we next see Turk (in the Archbishop's office), it is his left eye that is black and blue, not his right one.
When Gloria is escaping from Turk after beating him up in the abandoned apartment, she purposefully takes her purse from off her shoulder and drops it on the floor; she exits the room and closes the door behind her. In the following shot when she emerges in the next room from behind the just closed door, the purse is again draped over her shoulder.
Scarface takes Gloria by surprise in her apartment. From one camera angle he holds around her wrists with her hands close to each other. From another angle her hands are held apart, parallel to her shoulders.
When Gloria opens her shower curtains and discovers the bathroom window is open, it is clearly night/dark out, but seconds later when she is grabbed by Scarface, bright daylight is coming through the same window.
Dudley Moore's conducting isn't always consistent with the music. This may not be a goof. A real orchestra conductor is always half a beat ahead of the music. It would be incorrect for him to be completely in sync with the music.
After Gloria ejects J.J. MacKuen from her apartment window, he rolls down the streets of San Francisco in a trash barrel and is then launched through the air into an open manhole. It is clear that the person flying through the air and into the open hole is a stunt double since he is a very tall man whereas the character is actually a little man/midget.
When the car drives into the pizza parlor and the guy making a pizza crust tosses the dough high into the air and dives out of the way, you can see the dough land a short distance behind where he was standing. The next shot shows supposedly the same crust landing on a woman's face.